The Physics of the Sublunar Region:
Combination and Mixture

One very important class of phenomena to which the theory of
matter, form and substance was applicable was that associated with
what we would today call "chemical combination." The
centrality of this class of phenomena is apparent when we recall
that, according to Aristotle, all substances encountered in the
real world, including organic tissues, are compounds of the four
elements. It comes as no surprise, therefore, that Aristotle should
have inquired into the nature of chemical combination and the
status of the original ingredients in a compound. He distinguished
between a mechanical aggregate, in which the small particles of two
substances are situated side by side without loss of individual
identity, and a true blending of the ingredients into a homogenous
compound in which the original natures disappear; he called the
latter a "mixt" or "mixture" (we will employ
the Latin terms mixtio for the process and mixtum
[plural, mixta] for the product, in order to preserve the technical
meaning that Aristotle had in mind), and it is this kind of
combination that he considered applicable to the mixing of the
elements.

In a mixtum, according to Aristotle, the individual
natures of the ingredients are replaced by a new nature that
permeates the compound down to its smallest parts. The properties
of the mixtum represent an averaging of the properties of
the ingredients. If, for example, we combine a wet and a dry
element (say, water and earth), the wetness or dryness of the
resulting compound will fall on the scale that runs between the
extremes of wetness and dryness, at a point determined by the
relative abundance of those two qualities. Although the original
elements no longer have actual existence in the mixtum,
Aristotle made remarks that suggested that they remain a virtual or
potential presence that permits them to exercise some kind of
continuing influence.

Aristotle's discussion left a number of problems for his
commentators. One was to recast the theory of combination or
mixtio in the language and conceptual framework of matter
and form, for those terms do not appear in Aristotle's account.
In the course of that effort it was necessary to inquire how the
new substantial form of the mixtum emerges from the forms
of the constituent elements. Another problem of critical importance
was to determine in what sense the forms of the original elements
continue to exist in the mixtum; since it was acknowledged
that when the mixtum is destroyed the elements of which it
was formed reappear, it seemed evident that they survive in some
way within the mixtum. Debates on these matters became
extremely intricate, and we must limit ourselves to a few
remarks.

Everybody agreed that the substantial forms of the constituent
elements are replaced by a new substantial form of the
mixtum. Yet how does this come about? It was generally
agreed that the way was paved for the emergence of the new
substantial form by the mingling of the elements, the interaction
of their respective qualities, and possibly the corruption of their
substantial forms. However, there was good reasons (drawn from
Aristotle) for believing that the new substantial form could not be
generated out of these antecedent substantial forms or out of the
qualities of the original elements; outside intervention seemed to
be required. The usual solution was to invoke higher powers --
celestial forces or celestial intelligences, possibly even God
himself -- assigning to them the responsibility for infusing the
new substantial form into the primary matter when the preconditions
had been met.

As for survival of the elements in the mixtum,
everybody saw that it was necessary to find some way of allowing
the elements to lurk in the mixtum potentially or
virtually, awaiting a suitable opportunity to reveal themselves.
Avicenna argued that the forms of the elements survive intact,
while their qualities are weakened to the point of insensibility.
Averroes maintained that both the forms of the elements and their
qualities are reduced in strength or intensity and maintain a
potential existence within the mixtum. Since, according to
Aristotle, substantial forms do not admit of degrees -- that is,
cannot be strengthened or weakened (after all, a given four-legged
mammal is either a dog or not a dog; in this context talk of more
and less makes no sense) -- Averroes concluded that the forms of
the original elements must not be substantial forms but have a
status between that of substantial and accidental form. Thomas
Aquinas (ca. 1124-74) argued that the forms of the elements are
extinguished in the process of mixtio, but that their
qualities retains some kind of virtual influence in the
mixtum. These and other positions became the basis of
lively debate among late medieval natural philosophers.

A final question with which me must deal has to do with the
physical divisibility of corporeal substances -- say, wood or stone
or organic tissue. Is there a limit to the process of division, and
what are the properties of the smallest pieces? Are they anything
like atoms (here I refer to the ancient Greek concept, not the
modern)? Aristotle had alluded to the smallest pieces of the
ingredients of a mixtum, which mingle and interact, and on
these remarks subsequent commentators based a theory of what came
to be called minima or minima naturalia (smallest
natural parts). The theory acknowledged that in principle
divisibility should be endless; however small the piece before you,
there is no physical reason why you cannot divide it again.
However, it was argued that there is nonetheless a smallest
quantity of each substance, below which it will no longer be that
substance because the form of the substance cannot be preserved in
a smaller quantity.

There were attempts in the Middle Ages to construe the theory of
minima as a variant of atomism. It is true that both
theories acknowledged the particulate structure of matter, but
otherwise they were far apart. The particles of the atomists were
unbreakable least parts; the minima of the Middle Ages
were divisible, though if divided they would lose their identity.
All atoms were of identical stuff, differing only in size and
shape; minima were as different as the substances to which
they belonged. In the atomist vision, properties in the macroscopic
world did not, in general, have exact counterparts in the
microscopic world: atomists did not explain the redness of a
flower, for example, by the redness of its constituent particles.
Rather, the atomist program was the reduce the qualitative richness
of the world of sense experience to austere, qualitatively bare
atoms (characterized only by size, shape, motion and possibly
weight). Minimists, by contrast, continued the Aristotelian
program, assigning to the last parts precisely the properties of
the hole to which they integrally belonged: minima of wood
are still wood.